Process for tag imaging and decoding of machine readable coded data

ABSTRACT

Provided is a process for tag imaging and decoding of machine readable coded data which comprises a plurality of layouts. Each layout has at least order n rotational symmetry, where n is at least two. The layout encodes a first codeword comprising a sequence of at least n first symbols, the first symbols being distributed at n locations about a center of rotational symmetry of the layout such that decoding the first symbols at each of the n orientations of the layout produces n representations of the first codeword. Each representation includes a different cyclic shift of the first codeword and being indicative of the degree of rotation of the layout. Each representation also includes a second codeword comprising a number of second symbols, the second codeword being indicative of information regarding the respective layout. The process includes the steps of acquiring an image which includes said coded data, and identifying at least one layout. The process also includes decoding the layout to determine at least a representation of the first codeword, and determining a degree of rotation of the layout from the decoded representation.

CROSS REFERENCE TO RELATED APPLICATION

The present application is a Continuation of U.S. application Ser. No.12/202,296 filed on Aug. 31, 2008, which is a Continuation of U.S.application Ser. No. 10/893,372 filed on Jul. 19, 2004, now Issued U.S.Pat. No. 7,431,219, which is a Continuation of U.S. application Ser. No.10/409,864 filed on Apr. 9, 2003 now abandoned, the entire contents ofwhich are herein incorporated by reference.

FIELD OF INVENTION

This invention relates to orientation-indicating cyclic position codesand their use in the position-coding of surfaces.

CO-PENDING APPLICATIONS

Various methods, systems and apparatus relating to the present inventionare disclosed in the following US applications co-filed by the applicantor assignee of the present invention:

U.S. Ser. No. 7,111,791 entitled “Symmetric Tags”;

U.S. Ser. No. 7,156,289 entitled “Methods and Systems for ObjectIdentification and Interaction”;

U.S. Ser. No. 7,178,718 entitled “Methods and Systems for ObjectIdentification and Interaction”; and

U.S. Ser. No. 7,225,979 entitled “Methods and Systems for ObjectIdentification and Interaction”.

The disclosures of these co-filed applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following application filed by the applicant orassignee of the present invention on 7 Apr. 2003: Australian ProvisionalApplication No 2003901617 entitled “Methods and Systems for ObjectIdentification and Interaction”. The disclosures of this co-pendingapplication are incorporated herein by cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending PCT applications filed by theapplicant or assignee of the present invention on 4 Dec. 2002: U.S. Ser.No. 10/309,358 entitled “Rotationally Symmetric Tags”. The disclosuresof these co-pending applications are incorporated herein bycross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending PCT applications filed by theapplicant or assignee of the present invention on 22 Nov. 2002:

PCT/AU02/01572 and PCT/AU/02/01573.

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending PCT applications filed by theapplicant or assignee of the present invention on 15 Oct. 2002:

PCT/AU02/01391, PCT/AU02/01392, PCT/AU02/01393, PCT/AU02/01394 andPCT/AU02/01395.

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending PCT applications filed by theapplicant or assignee of the present invention on 26 Nov. 2001:

PCT/AU01/01527, PCT/AU01/01528, PCT/AU01/01529, PCT/AU01/01530 andPCT/AU01/01531.

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending PCT application filed by theapplicant or assignee of the present invention on 11 Oct. 2001:PCT/AU01/01274. The disclosures of this co-pending application areincorporated herein by cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending PCT application filed by theapplicant or assignee of the present invention on 14 Aug. 2001:PCT/AU01/00996. The disclosures of this co-pending application areincorporated herein by cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending US applications filed by theapplicant or assignee of the present invention on 27 Nov. 2000:

6,530,339 6,631,897 7,295,839 7,593,899 7,175,079 7,064,851 6,826,5476,741,871 6,927,871 6,980,306 6,965,439 6,788,982 7,263,270 6,788,2936,946,672 7,091,960 6,792,165 7,105,753 7,182,247

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending US applications filed by theapplicant or assignee of the present invention on 20 Oct. 2000:

7,190,474 7,110,126 6,813,558 6,965,454 6,847,883 7,131,058 7,533,0316,982,798 6,474,888 6,627,870 6,724,374 7,369,265 6,454,482 6,808,3306,527,365 6,474,773 6,550,997

The disclosures of these co-pending US applications are incorporatedherein by cross-eference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending US applications filed by theapplicant or assignee of the present invention on 15 Sep. 2000:

6,679,420 6,963,845 6,995,859 6,720,985

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending US applications filed by theapplicant or assignee of the present invention on 30 Jun. 2000:

6,824,044 6,678,499 6,976,220 6,976,035 6,766,942 7,286,113 6,922,7796,978,019 7,406,445 6,959,298 6,973,450 7,150,404 6,965,882 7,233,9247,007,851 6,957,921 6,457,883 6,831,682 6,977,751 6,398,332 6,394,5736,622,923

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

Various methods, systems and apparatus relating to the present inventionare disclosed in the following co-pending US applications filed by theapplicant or assignee of the present invention on 23 May 2000:

6,428,133 6,526,658 6,315,399 6,338,548 6,540,319 6,328,431 6,328,4256,991,320 6,383,833 6,464,332 6,390,591 7,018,016 6,328,417 09/575,1977,079,712 6,825,945 7,330,974 6,813,039 6,987,506 7,038,797 6,980,3186,816,274 7,102,772 7,350,236 6,681,045 6,728,000 7,173,722 7,088,45909/575,181 7,068,382 7,062,651 6,789,194 6,789,191 6,644,642 6,502,6146,622,999 6,669,385 6,549,935 6,987,573 6,727,996 6,591,884 6,439,7066,760,119 7,295,332 6,290,349 6,428,155 6,785,016 6,870,966 6,822,6396,737,591 7,055,739 7,233,320 6,830,196 6,832,717 6,957,768 7,456,8207,170,499 7,106,888 7,123,239 6,409,323 6,281,912 6,604,810 6,318,9206,488,422 6,795,215 7,154,638 6,859,289

The disclosures of these co-pending applications are incorporated hereinby cross-reference.

BACKGROUND

It is known to provide one or more coded data structures on a surfacethat can be read and decoded by a suitable sensing device. Variousembodiments of such a device incorporating an optical sensor aredescribed in many of the documents incorporated into the presentapplication by cross-reference.

The coded data structures disclosed in these documents include targetfeatures that enable the sensing device to identify the position of eachstructure. The relative positions of the features within each structurecan also be interpreted to determine perspective distortion of thestructure as sensed, enabling perspective correction to be performed onthe sensed data. However, to enable the sensing device to decode thedata in the structure, it is necessary that the rotational orientationof the structure be determined. Typically, this is achieved by providingat least one feature that is rotationally asymmetric in some way. Forexample, in one embodiment, a keyhole-shaped feature is provided thatcan be located with respect to the other features, and then recognisedto ascertain the rotational orientation of the structure in relation tothe sensing device. The actual data that is encoded in the datastructure can then be decoded, since its position in the data structurecan be inferred from the structure's position and rotationalorientation.

Disadvantages with this arrangement include the need to dedicate spaceto one or more orientation features, and the difficulty of includingredundancy in such features for the purposes of allowing rotationalorientation determination in the presence of damage to the features. Itis desirable, therefore, to encode orientation information both morespace-efficiently and in an error-detectable and/or error-correctablefashion.

SUMMARY OF THE INVENTION

According to an aspect of the present invention there is provided aprocess for tag imaging and decoding of machine readable coded datawhich comprises a plurality of layouts, each layout having at leastorder n rotational symmetry, where n is at least two, the layoutencoding a first codeword comprising a sequence of at least n firstsymbols, the first symbols being distributed at n locations about acenter of rotational symmetry of the layout such that decoding the firstsymbols at each of the n orientations of the layout produces nrepresentations of the first codeword, each representation comprising adifferent cyclic shift of the first codeword and being indicative of thedegree of rotation of the layout, and a second codeword comprising anumber of second symbols, the second codeword being indicative ofinformation regarding the respective layout, said process comprising:

acquiring an image which includes said coded data;

identifying at least one layout;

decoding the layout to determine at least a representation of the firstcodeword; and

determining a degree of rotation of the layout from the decodedrepresentation.

Other aspects are also disclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred and other embodiments of the invention will now be described,by way of non-limiting example only, with reference to the accompanyingdrawings, in which:

FIG. 1 shows a first embodiment of a tag structure according to theinvention;

FIG. 2 shows a symbol unit cell of the tag structure of FIG. 1;

FIG. 3 shows an array of symbol unit cells;

FIG. 4 is a schematic illustrating symbol bit ordering;

FIG. 5 shows the pattern of a tag with every bit set;

FIG. 6 shows the layout of an orientation-indicating cyclic positioncodeword;

FIG. 7 shows the layout of three local codewords;

FIG. 8 shows interleaved fragments, of distributed codewords D, E and Fwith a fragment of codeword D shown shaded;

FIG. 9 shows three adjacent tags P, Q and R containing a complete set ofdistributed codewords D, E and F with codeword D shown shaded;

FIG. 10 shows the continuous tiling of tags P, Q and R;

FIG. 11 shows the complete structure of three adjacent tags, includingtheir orientation cyclic position codewords, local codewords anddistributed codewords;

FIG. 12 shows the geometry of a tag segment;

FIG. 13 shows the preferred spacing d=(1−√3/2)s between tag segments,required to maintain consistent spacing between macrodots;

FIG. 14 shows the effect of the inter-segment spacing d on targetposition;

FIG. 15 shows the nominal relationship between the tag coordinate spaceand the surface x-y coordinate space;

FIG. 16 shows a tag coordinate grid superimposed on the tag tiling;

FIG. 17 shows a tag and its six immediate neighbours, each labelled withits corresponding bit index in the active area map and the input areamap;

FIG. 18 shows a preferred embodiment of a PEC unit cell compatible withthe present surface coding, superimposed on a tiling of tags;

FIG. 19 shows a preferred embodiment of a PEC unit cell superimposed onactual P, Q and R type tag structures;

FIG. 20 shows a preferred minimal imaging field of view required toguarantee acquisition of an entire tag; and

FIG. 21 shows a tag image processing and decoding process flow.

DESCRIPTION OF PREFERRED AND OTHER EMBODIMENTS

This document defines the surface coding used by the netpage system (asdisclosed in the present applicants' co-pending PCT applicationpublication number WO 01/22207—Method and System for Instruction of aComputer, the contents of which are herein incorporated by reference) toimbue otherwise passive surfaces with interactivity in conjunction withnetpage sensing devices such as the netpage pen (as disclosed in thepresent applicants' co-pending PCT application publication number WO00/72230—Sensing Device, the contents of which are herein incorporatedby reference) and the netpage viewer (as disclosed in the presentapplicants' co-pending PCT application publication number WO01/41046—Viewer with Code Sensor, the contents of which are hereinincorporated by reference).

When interacting with a netpage coded surface, a netpage sensing devicegenerates a digital ink stream which indicates both the identity of thesurface region relative to which the sensing device is moving, and theabsolute path of the sensing device within the region.

1. Surface Coding

The netpage surface coding consists of a dense planar tiling of tags.Each tag encodes its own location in the plane. Each tag also encodes,in conjunction with adjacent tags, an identifier of the regioncontaining the tag. In the netpage system, the region typicallycorresponds to the entire extent of the tagged surface, such as one sideof a sheet of paper.

Each tag is represented by a pattern which contains two kinds ofelements. The first kind of element is a target. Targets allow a tag tobe located in an image of a coded surface, and allow the perspectivedistortion of the tag to be inferred. The second kind of element is amacrodot. Each macrodot encodes the value of a bit by its presence orabsence.

The pattern is represented on the coded surface in such a way as toallow it to be acquired by an optical imaging system, and in particularby an optical system with a narrowband response in the near-infrared.The pattern is typically printed onto the surface using a narrowbandnear-infrared ink.

1.1 Tag Structure

FIG. 1 shows the structure of a complete tag 700. Each of the six blackcircles 702 is a target. The tag, and the overall pattern, is six-foldsymmetric at the physical level.

Each diamond-shaped region 704 represents a symbol, and each symbolrepresents four bits of information.

FIG. 2 shows the structure of a symbol. It contains four macrodots 706,each of which represents the value of one bit by its presence (one) orabsence (zero).

The macrodot spacing is specified by the parameter s throughout thisdocument. It has a nominal value of 143 μm, based on 9 dots printed at apitch of 1600 dots per inch. However, it may vary within defined boundsaccording to the capabilities of the device used to produce the pattern.

In general, if a surface is coded with a pattern which deviates from the“ideal” pattern specified in this document, e.g. due to devicelimitations, then the deviation must be recorded so that any digital inkcaptured via the surface can be appropriately corrected for thedeviation.

FIG. 3 shows an array of five adjacent symbols. The macrodot spacing isuniform both within and between symbols.

FIG. 4 shows the ordering of the bits within a symbol. Bit zero is theleast significant within a symbol; bit three is the most significant.Note that this ordering is relative to the orientation of the symbol.The orientation of a particular symbol within the tag is indicated bythe orientation of the label of the symbol in the tag diagrams (see FIG.1, for example). In general, the orientation of all symbols within aparticular segment of the tag have the same orientation, consistent withthe bottom of the symbol being closest to the centre of the tag.

In the preferred embodiment only the macrodots are part of therepresentation of a symbol in the pattern. The diamond-shaped outline ofa symbol is used in this document to more clearly elucidate thestructure of a tag. FIG. 5, by way of illustration, shows the actualpattern of a tag with every bit set. Note that, in the preferredembodiment, every bit of a tag can never be set in practice.

A macrodot is nominally circular with a nominal diameter of (5/9)s.However, it may vary within defined bounds according to the capabilitiesof the device used to produce the pattern.

A target is nominally circular with a nominal diameter of (17/9)s.However, it may vary within defined bounds according to the capabilitiesof the device used to produce the pattern.

Each symbol shown in the tag structure in FIG. 1 has a unique label.Each label consists of an alphabetic prefix and a numeric suffix.

1.2 Error. Detection and Correction

Assume the data to be coded is broken into k-symbol blocks, with theq-ary symbols taken from the Galois field GF(q). The collection of allpossible k-tuples m=(m₀, m₁, . . . , m_(k−1)) forms a vector space overGF(q), containing q^(k) possible vectors. A corresponding block errorcode C of length n consists of a set of M n-symbol codewords {c₀, c₁, .. . , c_(M−1)}, where M=q^(k) and n>k, with each codeword of the formc=(c₀, c₁, . . . , c_(n−1)). Given a data block to be encoded, theencoder maps the data block onto a codeword in C. Since the collectionof all possible n-tuples over GF(q) contains q^(n) vectors, but thereare only M=q^(k) codewords, the code contains redundancy. This isexpressed logarithmically by r=n−log_(q) M=n−k, the code rate R=k/n. Thecode C is a linear code if it forms a vector subspace over GF(q), i.e.if it is closed under addition and under multiplication by a scalar (andthus contains the zero vector). The code is then said to have dimensionk and is referred to as an (n, k) code.

The Hamming distance between two codewords is the number of symbols inwhich the two codewords differ. The minimum distance d_(min) of a blockcode is the smallest Hamming distance of any pair of distinct codewordsin the code. The maximum distance d_(max) is the largest Hammingdistance of any pair of distinct codewords in the code.

An error pattern introduces symbol errors into a codeword. It ischaracterized by its weight, i.e. the number of symbols it corrupts. Foran error pattern to be undetectable, it must cause a codeword to looklike another codeword. A code with a minimum distance of d_(min) canthus detect all error patterns of weight less than or equal tod_(min)−1. Although a given code can detect many error patterns withgreater weights, this provides a limit on the weight for which a codecan detect all error patterns.

Given a sampled word possibly corrupted by an error pattern, the decodermaps the sampled word onto a codeword in C in such a way as to minimizethe probability that the codeword is different from the codewordoriginally written, and then maps the codeword onto a data block. In theabsence of a more specific characterization, it is assumed thatlower-weight error patterns are more likely than higher-weight errorpatterns, and that all error patterns of equal weight are equallylikely. The maximum likelihood written codeword is thus the codewordwhich is closest in Hamming distance to the sampled word. If the sampledword is closer to an incorrect codeword than the correct (written)codeword, then the decoder commits an error. Since codewords are bydefinition at least a distance d_(min) apart, decoder errors are onlypossible if the weight of the error pattern is greater than or equal tod_(min)/2. A maximum likelihood decoder can thus correct all errorpatterns of weight less than or equal to └(d_(min)−1)/2┘. Equivalently,the decoder can correct t errors so long as 2t<d_(min).

The minimum distance of a linear code is limited by the Singleton bound:d_(min)≦n−k+1. Codes which satisfy the Singleton bound with equality arecalled maximum-distance separable (MDS). Reed-Solomon codes (see Wicker,S. B. and V. K. Bhargava, eds., Reed-Solomon Codes and TheirApplications, IEEE Press, 1994, the contents of which are hereinincorporated by reference) are the most commonly-used MDS codes. Nobinary codes are MDS.

An erasure is a symbol of a sampled word assumed to have been corrupted.Since its position in the codeword is known, it can be ignored for thepurposes of decoding rather than being treated as an error. For example,the distance between the erased symbol in the sampled word and thecorresponding symbol in a codeword is not included in the Hammingdistance used as the basis for maximum likelihood decoding. Each erasurethus effectively reduces the minimum distance by one, i.e., in thepresence of f erasures, up to └(d_(min)−f−1)/2┘ errors can be corrected.Equivalently, the decoder can correct t errors and f erasures so long as2t+f<d_(min). For an MDS code this becomes 2t+f<n−k+1.

A code is systematic if each of its codewords contains, withoutmodification, its corresponding data block at a fixed location. It isthen possible to distinguish between the data (or message) coordinatesof the code and the redundancy (or parity) coordinates of the code.

The rate of a linear code can be increased by puncturing the code, i.e.by deleting one or more of its redundancy coordinates. By the deletionof g coordinates, an (n, k) code is transformed into an (n−g, k) code.The minimum distance of the punctured code is d_(min)−g Clearly, ifd_(min)−g<2, puncturing destroys the code's ability to correct even oneerror, while if d_(min)−g<1, it destroys the code's ability to detecteven one error. Equivalently, the length w=n−g of the punctured codemust obey w≧n−d_(min)+1 to be error-detecting, and w≦n−d_(min)+2 to beerror-correcting. The decoder for a punctured code can simply treatdeleted coordinates as erasures with respect to the original code.

A block code C is a cyclic code if for every codeword c=(c₀, c₁, . . . ,c_(n−2), c_(n−1))εC, there is also a codeword c′=(c_(n−1), c₀, c₁,c_(n−2))εC, i.e. c′ is a right cyclic shift of c. It follows that all ncyclic shifts of c are also codewords in C. If the number of codewordsq^(k) exceeds the length of the code n, then the code contains a numberof distinct cycles, with each cycle i containing s_(i) unique codewords,where s_(i) divides n. If the code contains the zero vector, then thezero vector forms its own cycle.

1.3 Orientation-Indicating Cyclic Position Code

The tag contains a 2⁴-ary (6, 1) cyclic position codeword (as disclosedin the present Applicants' co-pending PCT application publication numberWO 02/084473—Cyclic Position Codes, the contents of which are hereinincorporated by reference) which can be decoded at any of the sixpossible orientations of the tag to determine the actual orientation ofthe tag. Symbols which are part of the cyclic position codeword have aprefix of “R” and are numbered 0 to 5 in order of increasingsignificance.

The cyclic position codeword is (0, 5, 6, 9, A₁₆, F₁₆). Note that itonly uses six distinct symbol values, even though a four-bit symbol hassixteen possible values. Any unused symbol value detected duringdecoding is treated as an erasure. Note that the actual symbol orderingwithin the codeword is not critical, nor is the composition of thesubset of symbol values actually used. However, it is advantageous tochose a subset which maximises the minimum inter-symbol distance, sincethis helps ensure that a bit error is more likely to cause an erasurethan a symbol error. This is advantageous because the erasure-correctingcapacity of the code is roughly twice its error-correcting capacity (asdiscussed below).

The layout of the orientation-indicating cyclic position codeword isshown in FIG. 6 in which the codeword is shown shaded.

The minimum distance of the cyclic position code is 6, hence itserror-correcting capacity is two symbols in the presence of up to oneerasure, one symbol in the presence of two or three erasures, and nosymbols in the presence of four or more erasures.

Table 1 shows the Hamming distance between the first codeword of thecyclic position code and each of the codewords of the code, computedwith a single symbol error successively in each of the six possiblelocations in the codeword. In each case the corrupted symbol isindicated by ♦. For worst-case purposes the symbol is assumed to havebeen corrupted to the corresponding symbol of each of the othercodewords. Whereas the distance between the corrupted codeword and itsuncorrupted original is one in each case, the distance between thecorrupted codeword and each of the other codewords is five in each case.Since every codeword is some cyclic shift of the first codeword, thetable demonstrates the ability of the code to correct any single symbolerror in any codeword.

By extension, it can be seen that in the presence of any two symbolerrors the distance between the corrupted codeword and its uncorruptedoriginal increases to two in each case, and the distance between thecorrupted codeword and each of the other codewords decreases to four ineach case. The table therefore also demonstrates the ability of the codeto correct any double symbol errors in any codeword. This is illustratedin Table 2.

TABLE 1 Cyclic position code distances in the presence of one errorcodeword 0569AF 569AF0 69AF05 9AF056 AF0569 F0569A 0569A♦ 1 5 5 5 5 50569♦F 1 5 5 5 5 5 056♦AF 1 5 5 5 5 5 05♦9AF 1 5 5 5 5 5 0♦69AF 1 5 5 55 5 ♦569AF 1 5 5 5 5 5

TABLE 2 Cyclic position code distances in the presence of two errorscodeword 0569AF 569AF0 69AF05 9AF056 AF0569 F0569A 0569♦♦ 2 4 4 4 4 4056♦♦F 2 4 4 4 4 4 05♦♦AF 2 4 4 4 4 4 0♦♦9AF 2 4 4 4 4 4 ♦♦69AF 2 4 4 44 4 ♦569A♦ 2 4 4 4 4 4

The same distance calculations can be performed in the presence of oneor more erasures by simply ignoring the erased coordinate(s). This isillustrated in Table 3, where a single erasure is indicated by—.

TABLE 3 Cyclic position code distances in the presence of one error andone erasure codeword −569AF −69AF0 −9AF05 −AF056 −F0569 −0569A −569A♦ 14 4 4 4 4 −569♦F 1 4 4 4 4 4 −56♦AF 1 4 4 4 4 4 −5♦9AF 1 4 4 4 4 4−♦69AF 1 4 4 4 4 4 −569AF 0 5 5 5 5 5

Decoding a sampled cyclic position codeword consists of detecting anyerasures and then calculating the distance between the remaining(un-erased) symbols and the corresponding symbols in the six cyclicshifts of the original cyclic position codeword. The sampled codeword isthen decoded as the shifted codeword which is closest in distance fromthe sampled codeword. Decoding fails if more than one shifted codewordis equally closest to the sampled codeword. Once the sampled codeword isdecoded to a shifted codeword, the shift of that codeword is known andthus the rotation of the tag with respect to the sampling orientationknown.

In addition to the six symbols which form the cyclic position codeword,at least an additional six symbols of adjacent tags' cyclic positioncodewords are also visible within the field of view. At the addedexpense of decoding these extra symbols, twelve symbols may be used todecode the cyclic position codeword. This may be done in two ways. Inthe first approach every erased symbol is simply replaced by itscorresponding symbol from one of the other tags' cyclic positioncodewords, if the corresponding symbol has not itself been erased. Inthe second approach, all twelve symbols are treated as a twelve-symbolcodeword.

The cyclic position code can also be used to detect whether the tag hasbeen acquired mirror reflected, e.g. when the tag is imaged through theback of a transparent substrate on which it is disposed.

1.4 Local Codewords

The tag locally contains three complete codewords which are used toencode information unique to the tag. Each codeword is of a punctured2⁴-ary (9, 5) Reed-Solomon code. The tag therefore encodes up to 60 bitsof information unique to the tag.

The layout of the three local codewords is shown in FIG. 7 in whichcodeword A is shown shaded.

1.5 Distributed Codewords

The tag also contains fragments of three codewords which are distributedacross three adjacent tags and which are used to encode informationcommon to a set of contiguous tags.

Each codeword is of a punctured 2⁴-ary (9, 5) Reed-Solomon code. Anythree adjacent tags therefore together encode up to 60 bits ofinformation common to a set of contiguous tags.

The layout of the three codeword fragments is shown in FIG. 8.

The layout of the three complete codewords, distributed across threeadjacent tags, is shown in FIG. 9. In relation to these distributedcodewords there are three types of tag. These are referred to as P, Qand R in order of increasing significance.

FIG. 10 shows how the P, Q and R tags are repeated in a continuoustiling of tags. The tiling guarantees the any set of three adjacent tagscontains one tag of each type, and therefore contains a complete set ofdistributed codewords. The tag type, used to determine the registrationof the distributed codewords with respect to a particular set ofadjacent tags, is encoded in one of the local codewords of each tag.

FIG. 11 shows the complete structure of three adjacent tags, includingtheir orientation cyclic position codewords, local codewords anddistributed codewords.

FIG. 12 shows the geometry of a tag segment 708.

FIG. 13 shows the spacing d=(1−√3/2)s between tag segments, required tomaintain consistent spacing between macrodots.

FIG. 14 shows the effect of the inter-segment spacing d on targetposition. Compared with their nominal positions in relation toclosely-packed segments (i.e. with d=0), diagonal targets must bedisplaced by (Δ_(x), Δ_(y))=(±1/√3, ±1)d, and horizontal targets must bedisplaced by (Δ_(x), Δ_(y))=(±2/√3, 0)d.

1.6 Reed-Solomon Encoding

Both local and distributed codewords are encoded using a punctured2⁴-ary (9, 5) Reed-Solomon code.

A 2⁴-ary (9, 5) Reed-Solomon code encodes 20 data bits (i.e. five 4-bitsymbols) and 16 redundancy bits (i.e. four 4-bit symbols) in eachcodeword. Its error-detecting capacity is four symbols. Itserror-correcting capacity is two symbols.

A punctured 2⁴-ary (9, 5) Reed-Solomon code is a 2⁴-ary (15, 5)Reed-Solomon code with six redundancy coordinates removed.

The code has the following primitive polynominal:p(x)=x ⁴ +x+1

The code has the following generator polynominal:g(x)=(x+α)(x+α ²) . . . (x+α ¹⁰)

For a detailed description of Reed-Solomon codes, refer to Wicker, S. B.and V. K. Bhargava, eds., Reed-Solomon Codes and Their Applications,IEEE Press, 1994.

2. Tag Coordinate Space

The tag coordinate space 710 is defined by a pair of semi-orthogonalcoordinates a and b. The nominal relationship between the tag coordinatespace and the surface x-y coordinate space is illustrated in FIG. 15.

The coordinates are necessarily only semi-orthogonal to ensurereproducibility of the tag pattern by intended printing devices (asdiscussed below under the heading “Encoding and PrintingConsiderations”).

To further assist intended printing devices, the surface coding, andhence the a-b coordinate space, is allowed to be rotated an arbitrarymultiple of 90 degrees with respect to the x-y coordinate space.

Given an anti-clockwise rotation R of the a-b coordinate space withrespect to the x-y coordinate space, the relations between the twocoordinates spaces are:

$\begin{matrix}{x = {{{a\cos}\left( {{30{^\circ}} - R} \right)} - {b\;{\sin\left( {{60{^\circ}} - R} \right)}}}} & \left( {{EQ}\mspace{14mu} 1} \right) \\{y = {{{a\sin}\left( {{30{^\circ}} - R} \right)} - {b\;{\cos\left( {{60{^\circ}} - R} \right)}}}} & \left( {{EQ}\mspace{14mu} 2} \right) \\{a = {\frac{x}{2{\cos\left( {{30{^\circ}} - R} \right)}} + \frac{y}{2{\sin\left( {{30{^\circ}} - R} \right)}}}} & \left( {{EQ}\mspace{14mu} 3} \right) \\{b = {\frac{- x}{2{\sin\left( {{60{^\circ}} - R} \right)}} + \frac{y}{2{\cos\left( {{60{^\circ}} - R} \right)}}}} & \left( {{EQ}\mspace{14mu} 4} \right)\end{matrix}$

Integer a and b coordinates are defined to intersect at the centres of Ptags, as illustrated in FIG. 16. The figure shows lines 714 and 712representing iso-lines of integer a and b coordinates respectively.

Note that the surface coding does not specify the location of the x-y(or a-b) origin on a particular tagged surface, or the orientation ofthe x-y (or a-b) coordinate space with respect to the surface. It onlydefines the relationship between the two coordinate spaces. Thismanifests itself in the x-y coordinates embedded in digital inkgenerated by a netpage sensing device used to interact with a netpagetagged surface.

3. Tag Information Content

Table 4 defines the information fields embedded in the surface coding.Table 5 defines how these fields map to local and distributed codewords.

TABLE 4 Field definitions field width description tag type 2 Defineswhether the tag is of type P (b′00′), Q (b′01′) or R (b′10′). tag format2 The format of the tag information, b′00′ indicates the formatspecified in this table. All other values are reserved. local flag 1Indicates whether the region ID is owned by a local netpage system(b′1′) or the global netpage system (b′0′). active area 7 A map¹ ofwhich of the tag and its immediate map neighbours are members of anactive area; b′1′ indicates membership. input area 7 A map^(a) of whichof the tag and its immediate map neighbours are members of an inputarea; b′1′ indicates membership. coordinate 5 The precision of the a andb coordinates; precision valid range is 0 to 20. (w) a w The signed acoordinate of the tag, coordinate (0 to 20) in sign-magnitude format. bw The signed b coordinate of the tag, coordinate (0 to 20) insign-magnitude format. region ID 96 − 2w The ID of the region containingthe tags. (96 to 56)  Total 120  ¹FIG. 17 indicates the bit ordering ofthe map.

FIG. 17 shows a tag and its six immediate neighbours, each labelled withits corresponding bit index in the active area map and the input areamap.

Since the top 55 bits of the region ID are encoded in distributedcodewords, they are by necessity constant for an entire contiguoustiling of tags. The bottom 41 bits, however, are encoded in localcodewords, and so may vary arbitrarily from one tag to the next.

For a particular surface coding, the number of bits dedicated to the aand b coordinates is configurable via the coordinate precision field. Inthis way the precision can be tuned to the size of the surface beingtagged, which in turn allows efficient use of a higher-precision regionID space. Region IDs can be allocated from the full-precision 95-bitspace, but with the constraint that for a particular coordinateprecision of w, the bottom 2w bits of each allocated region ID must bezero. Almost equivalently, different-precision region IDs can beallocated from precision-specific pools, and each allocated region IDcan be indexed and looked-up in a pool-specific way.

TABLE 5 Mapping of fields to codewords codeword field field codewordwidth bits bits tag type A 2  1:0 all tag format 2  3:2 all local flag 1 4 all active area map 7 11:5 all input area map 7  18:12 all coordinateprecision (w) D 5  19:15 all a coordinate B w (w − 1):0 all b coordinateC w (w − 1):0 all region ID D 15  14:0 95:81 E 20  19:0 80:61 F 20  19:060:41 A 1 19 40 B 20 − w 19:w² 39:(20 + w)^(a) C 20 − w 19:w^(a) (19 +w):2w^(a) ²if w < 20

The active area map indicates whether the corresponding tags are membersof an active area. An active area is an area within which any capturedinput should be immediately forwarded to the corresponding netpageserver for interpretation. It also allows the netpage sensing device tosignal to the user that the input will have an immediate effect.

The input area map indicates whether the corresponding tags are membersof an input area, i.e. lie within the extent of a form. It allows thenetpage sensing device to signal to the user that the input will besubmitted to an application.

4. Encoding and Printing Considerations

The Print Engine Controller (PEC) (as disclosed in the presentApplicants' co-pending PCT application publication numbers WO01/89851—Print Engine/Controller and Printhead Interface ChipIncorporating the Print Engine/Controller and WO 01/89838—Printed PageTag Encoder, the contents of both of which are herein incorporated byreference) supports the encoding of two fixed (per-page) 2⁴-ary (15, 5)Reed-Solomon codewords and six variable (per-tag) 2⁴-ary (15, 5)Reed-Solomon codewords. Furthermore, PEC supports the rendering of tagsvia a rectangular unit cell whose layout is constant (per page) butwhose variable codeword data may vary from one unit cell to the next.PEC does not allow unit cells to overlap in the direction of pagemovement.

FIG. 18 shows a preferred embodiment of a PEC unit cell 718 compatiblewith the present surface coding, superimposed on a tiling of tags. FIG.19 shows the proposed PEC unit cell superimposed on actual P, Q and Rtype tag structures. Note that the proposed unit cell is centeredhorizontally on a P type tag. The tag structure and unit cell aredesigned so that the unit cell contains exactly six variable codewords(i.e., for row n, R_(n):A, P_(n):A, Q_(n):A, {R,P,Q}_(n):B,{R,P,Q}_(n):C, and {R,P,Q}_(n+1):B), and three fixed codewords D, E andF.

At least one of codewords D, E and F must be pre-encoded in the TagFormat Structure (TFS) passed to PEC, since PEC only supports theencoding of two fixed codewords. Any or all of codewords D, E and Fcould be pre-encoded in the TFS.

PEC imposes a limit of 32 unique bit addresses per TFS row. The contentsof the unit cell respect this limit, assuming pre-encoding of D, E and Fcodewords.

PEC also imposes a limit of 384 on the width of the TFS. The contents ofthe unit cell respect this limit.

Note that for a reasonable page size, the number of variable coordinatebits in the B and C codewords is modest, making encoding via a lookuptable tractable. Encoding of the A codeword via a lookup table may alsobe possible. Note that since a Reed-Solomon code is systematic, only theredundancy data needs to appear in the lookup table.

5. Imaging and Decoding Considerations

FIG. 20 shows a preferred minimal imaging field of view 720 required toguarantee acquisition of an entire tag, i.e. given arbitrary alignmentbetween the surface coding and the field of view.

The diameter of the minimal field of view is 36 s

Given the present tag structure, the corresponding decoding sequence isas follows:

-   -   locate targets of complete tag    -   infer perspective transform from targets    -   sample cyclic position code    -   decode cyclic position code    -   determine orientation from cyclic position code    -   sample local Reed-Solomon codewords    -   decode local Reed-Solomon codewords    -   determine tag type    -   determine tag rotation    -   sample distributed Reed-Solomon codewords (modulo window        alignment, with reference to tag type)    -   decode distributed Reed-Solomon codewords    -   determine coordinate precision    -   determine region ID    -   determine tag a-b location    -   transform tag a-b location to x-y location, with reference to        tag rotation    -   infer 3D transform from oriented targets    -   determine nib x-y location from tag x-y location and 3D        transform    -   determine active/input area status of nib location    -   generate local feedback based on nib active/input area status    -   encode region ID, nib x-y location, nib active/input area status        in digital ink

FIG. 21 shows a tag image processing and decoding process flow. A rawimage 802 of the tag pattern is acquired (at 800), for example via animage sensor such as a CCD image sensor, CMOS image sensor, or ascanning laser and photodiode image sensor. The raw image is thentypically enhanced (at 804) to produce an enhanced image 806 withimproved contrast and more uniform pixel intensities. Image enhancementmay include global or local range expansion, equalisation, and the like.The enhanced image 806 is then typically filtered (at 808) to produce afiltered image 810. Image filtering may consist of low-pass filtering,with the low-pass filter kernel size tuned to obscure macrodots but topreserve targets. The filtering step 808 may include additionalfiltering (such as edge detection) to enhance target features. Thefiltered image 810 is then processed to locate target features (at 812),yielding a set of target points. This may consist of a search for targetfeatures whose spatial inter-relationship is consistent with the knowngeometry of a tag. Candidate targets may be identified directly frommaxima in the filtered image 810, or may the subject of furthercharacterisation and matching, such as via their (binary or grayscale)shape moments (typically computed from pixels in the enhanced image 806based on local maxima in the filtered image 810), as described in U.S.patent application Ser. No. 09/575,154. The search typically starts fromthe center of the field of view. The target points 814 found by thesearch step 812 indirectly identify the location of the tag in thethree-dimensional space occupied by the image sensor and its associatedoptics. Since the target points 814 are derived from the (binary orgrayscale) centroids of the targets, they are typically defined tosub-pixel precision.

It may be useful to determine the actual 3D transform of the tag (at816), and, by extension, the 3D transform (or pose) 818 of the sensingdevice relative to the tag. This may be done analytically, as describedin U.S. patent application Ser. No. 09/575,154, or using a maximumlikelihood estimator (such as least squares adjustment) to fit parametervalues to the 3D transform given the observed perspective-distortedtarget points (as described in P. R. Wolf and B. A. Dewitt, Elements ofPhotogrammetry with Applications in GIS, 3rd Edition, McGraw Hill,February 2000, the contents of which are herein incorporated byreference thereto). The 3D transform includes the 3D translation of thetag, the 3D orientation (rotation) of the tag, and the focal length andviewport scale of the sensing device, thus giving eight parameters to befitted, or six parameters if the focal length and viewport scale areknown (e.g. by design or from a calibration step). Each target pointyields a pair of observation equations, relating an observed coordinateto a known coordinate. If eight parameters are being fitted, then fiveor more target points are needed to provide sufficient redundancy toallow maximum likelihood estimation. If six parameters are being fitted,then four or more target points are needed. If the tag design containsmore targets than are minimally required to allow maximum likelihoodestimation, then the tag can be recognised and decoded even if up tothat many of its targets are damaged beyond recognition.

To allow macrodot values to be sampled accurately, the perspectivetransform of the tag must be inferred. Four of the target points aretaken to be the perspective-distorted corners of a rectangle of knownsize in tag space, and the eight-degree-of-freedom perspective transform822 is inferred (at 820), based on solving the well-understood equationsrelating the four tag-space and image-space point pairs (see Heckbert,P., Fundamentals of Texture Mapping and Image Warping, Masters Thesis,Dept. of EECS, U. of California at Berkeley, Technical Report No.UCB/CSD 89/516, Jun. 1989, the contents of which are herein incorporatedby reference thereto). The perspective transform may alternatively bederived from the 3D transform 818, if available.

The inferred tag-space to image-space perspective transform 822 is usedto project (at 824) the known position of each data bit of theorientation-indicating cyclic position codeword from tag space intoimage space where the real-valued position is used to bi-linearly (orhigher-order) interpolate (at 824) the four (or more) relevant adjacentpixels in the enhanced input image 806. The resultant macrodot value iscompared with a suitable threshold to determine whether it represents azero bit or a one bit. For sampling purposes, the spatial layout of theorientation-indicating cyclic position codeword is fixed, and isorientation-invariant.

Once the bits of the complete orientation-indicating cyclic positioncodeword have been sampled, the orientation-indicating codeword isdecoded (at 830), as previously described, to obtain the orientation 832of the tag relative to the sampling orientation.

The inferred tag-space to image-space perspective transform 822 is usedto project (at 834) the known position of each data bit of the local anddistributed codewords from tag space into image space where thereal-valued position is used to bi-linearly (or higher-order)interpolate (at 834) the four (or more) relevant adjacent pixels in theenhanced input image 806. The resultant macrodot value is compared witha suitable threshold to determine whether it represents a zero bit or aone bit. For sampling purposes, the spatial layout of the local anddistributed codewords is fixed, but is orientation-specific. Theorientation 832 is therefore used to determine the actual orientation ofthe layout.

Once the bits of one or more complete codewords have been sampled, thecodewords are decoded (at 838) to obtain the desired data 840 encoded inthe tag. Redundancy in the codeword may be used to detect errors in thesampled data, or to correct errors in the sampled data.

As discussed in U.S. patent application Ser. No. 09/575,154, theobtained tag data 840 may directly or indirectly identify the surfaceregion containing the tag and the position of the tag within the region.An accurate position of the sensing device relative to the surfaceregion can therefore be derived from the tag data 840 and the 3Dtransform 818 of the sensing device relative to the tag.

CONCLUSION

Although the invention has been described with reference to a number ofspecific examples, it will be appreciated by those skilled in the artthat the invention can be embodied in many other forms.

1. A process for tag imaging and decoding of machine readable coded datawhich comprises a plurality of layouts, each layout having at leastorder n rotational symmetry, where n is at least two, the layoutencoding a first codeword comprising a sequence of at least n firstsymbols, the first symbols being distributed at n locations about acenter of rotational symmetry of the layout such that decoding the firstsymbols at each of the n orientations of the layout produces nrepresentations of the first codeword, each representation comprising adifferent cyclic shift of the first codeword and being indicative of thedegree of rotation of the layout, and a second codeword comprising anumber of second symbols, the second codeword being indicative ofinformation regarding the respective layout, said process comprising:acquiring an image which includes said coded data; identifying at leastone layout; decoding the layout to determine at least a representationof the first codeword; and determining a degree of rotation of thelayout from the decoded representation.
 2. The process of claim 1,wherein the step of identifying the layout includes processing the imageto locate one or more target features of the coded data, and determininga position of at least one of the encoded first symbols of the firstcodeword.
 3. The process of claim 1, wherein the step of acquiring theimage is carried out with an image sensor.
 4. The process of claim 3,wherein the image sensor is selected from a group consisting of a CCDimage sensor, a CMOS image sensor, a scanning laser image sensor, and aphotodiode image sensor.
 5. The process of claim 1, wherein thecodewords are determined once bits of one or more complete codewordshave been sampled, with redundancy present in the codewords used todetect errors in sampled data.
 6. The process of claim 1, furthercomprising the step of range expanding pixel values of the image.
 7. Theprocess of claim 1, further comprising the step of equalizing pixelvalues of the image.
 8. The process of claim 1, further comprising thestep of low-pass filtering the mage, with a low-pass filter kernel sizetuned to obscure macrodots whilst preserving coded data.